Damage sizes, i.e. all damages occurring to a policy and not only those that are reported to an insurance company, are modelled as a linear mixed model. Only those damages that are larger than their deductibles are reported to the company, and this fact should be taken into account when...

A methodology for fitting general stochastic volatility (SV) models that are naturally cast in terms of a positive volatility process is developed. Two well known methods for evaluating the likelihood function, sequential importance sampling and Laplace importance sampling, are combined. The...

We study the distribution of the stochastic integral [integral operator]0t8e-Rt dPt where R is a Brownian motion with positive drift and P is an independent compound Poisson process. We show that in the special case when the jumps of P are exponentially distributed, the integral has the same...

We introduce a general model to describe the risk process of an insurance company. This model allows for stochastic rate of return on investments as well as stochastic level of inflation, thus in theory enabling a decision maker to choose between insurance and investment risk. In the first part...

We study the distribution of the stochastic integral [integral operator][infinity]0e-RtdPt where P and R are independent Lévy processes with a finite number of jumps on finite time intervals. The exact distribution is obtained in many special cases, and we derive asymptotic properties of the...

We consider a classical risk process compounded by another independent process. Both of these component processes are assumed to be Lévy processes. Sharp conditions are given on the parameters of these two components to ensure when ruin is certain, and also when the time of ruin is of...